A hyperbolicity criterion for a class of diffeomorphisms of an infinite-dimensional torus. (1st February 2022)

• Record Type: Journal Article
• Authors: Glyzin, S. D.; Kolesov, A. Yu.
• Is Part Of: Sbornik. Volume 213:Number 2(2022)
• Page Start: 173
• Page End: 215
• Publication Date: 2022-02-01
• Subjects: 37D20 -- 46T20; 37E30 -- 58B20; map -- hyperbolicity -- infinite-dimensional torus -- Anosov diffeomorphism; Mathematics -- Periodicals; 510.5
• DOI: 10.1070/SM9535
• Languages: English
• ISSNs: 1064-5616

Abstract

Abstract: On an infinite-dimensional torus, where is an infinite-dimensional real Banach space and is an abstract integer lattice, a special class of diffeomorphisms is considered. It consists of the maps equal to sums of invertible bounded linear operators preserving and -smooth periodic additives. Necessary and sufficient conditions ensuring that such maps are hyperbolic (that is, are Anosov diffeomorphisms) are obtained. Bibliography: 15 titles.